What is the probability that a randomly selected box of the cereal contains less than 9.65 ounces of cereal

The equation which correctly represents the explicit formula for the nth term of the given sequence is; a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.

As evident in the task content; the given sequence is a geometric sequence and the common ratio of the sequence can be determined as;

r = 3 / 9 = 9 / 27 = 1 / 3.

On this note, since the common ratio of the consecutive terms of the sequence is; 1/3 it follows that the required explicit formula which represents the nth term , a (n) is;

a (n) = a (n - 1) × ( 1 / 3 ) and a (1) = 27.

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Answer: 35

Step-by-step explanation:

: i took this quiz before :)

We know that the area of a square/rectangle is the multiplication of its length by its width. We also know that this specific area does not include the blank region, therefore we need to subtract it from the area of the shaded region!

We can come up with two expressions:

Shaded Area:

[tex](5x + 2)(3x - 1)\\= 15x^2-5x+6x-2\\=15x^2+x-2[/tex]

Blank area:

[tex](x)(x+7)\\x^2+7x[/tex]

Now all we have to do is subtract the blank area's expression from the shaded area's and simplify since the question asks for the simplest form.

[tex](15x^2+x-2)-(x^2+7x)\\15x^2-x^2+x-7x-2\\14x^2-6x-2[/tex]

Therefore, your final answer should be:

14x^2 - 6x - 2

The distance of each chord from the centre of the circle are √119  and √128 respectively .

Given,

Radius of a circle = 12 cm

AB = 10 cm

CD = 8 cm

Now, we get

BG = 10/2 = 5 cm

HD = 8/2 = 4 cm

(A perpendicular coming from the centre, which is not a diameter, bisects the chord.)

Now,

BE = ED = EF = 12 cm (All radii of a circle are equal.)

Now, by Pythagoras Theorem, we get

H² = P² + B²

For GE —

(BE)² = (GE)² + (BG)²

or, (12)² = GE² + (5)²

or, 144 = GE² + 25

or, GE² = 144 — 25

or, GE² = 119

or GE = ±√119

or GE = √119 (Since, length cannot be negative.)

For HE —

(DE)² = (HE)² + (HD)²

or, (12)² = HE² + (4)²

or, 144 = HE² + 16

or, HE² = 144 — 16

or, HE² = 128

or, HE = ± √128

or, HE = √128 or 8√2(Since, length cannot be negative.)

Hence , the distance of each chord from the centre of the circle are √119  and √128 respectively .

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Cheri collected 145 number of 5 peso coin and 156 number of 10 peso coin during her family's annual outreach

An equation is used to show the relationship between numbers and variables.

Let x represent the number of 5 peso coins and y represent the number of 10 peso coin

At the end of the year, she has saved a total of Php 2285, hence:

5x + 10y = 2285    (1)

Also, she has 11 more 10 pesos than 5 peso coins, hence:

y = x + 11    (2)

Solving both equations using elimination method gives:

x = 145, y = 156

Cheri had 145 number of 5 peso coin and 156 number of 10 peso coin.  

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Answer:

by using sine rule and cosine rule.

The three types of algorithms are Brute Force algorithm, Greedy algorithm and Recursive algorithm.

As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search entails iteratively listing all potential candidates for the solution and determining if each one satisfies the problem's statement.

In order to find the divisors of a natural number n, a brute-force algorithm would count all integers from 1 to n & determine whether each one divides n without leaving a remainder.

A brute-force method might look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece may engage in mutually exclusive attacks for each configuration for the eight queens puzzle.

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Answer:

m∠A=126°

Step-by-step explanation:

Supplementary means that they add up to 180°.

Therefore we can do 180-54 to get 126° for the m∠A.

Hope this helped! :)

The triangle with sides of length 5 cm 3 cm and 4 cm is a right angled triangle because (3, 4, 5) is a Pythagorean triple.

We know that if non zero real numbers a, b, c follows Pythagoras theorem  c² = a² + b², the numbers a, b, c is called as a Pythagorean triple.

And these numbers are nothing but the sides of right triangle.

Here we have been given the triangle with sides of length 5 cm 3 cm and 4 cm

Assume that p = 5 cm, q = 3 cm and r = 4 cm

p² = 25

q² = 9

and r² = 16

Consider q² + r² = 16 + 9

q² + r² = 25

q² + r² = r²

Since given numbers follows Pythagoras theorem, (3, 4, 5) is a  Pythagorean triple.

And p = 5 cm, q = 3 cm and r = 4 cm are the lengths of sides of right triangle.

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On solving the provided question, we can say that An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant.

Arithmetic sequences are groups of integers that are arranged in a certain order and share a common difference between each term. The tolerance, for instance, is six in the mathematical progression 3, 9, 15, 21, and 27. Arithmetic progression can also be referred to as such. a series that is produced by adding the same value repeatedly. for instance, 1, 4, 7, 10, 13, 16, 19, 22, and 25. Sequences that have an arithmetic difference between two successive phrases are known as arithmetic sequences. A progression in math with a tolerance of 2 is 2,4,6,8,10.

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant. 2,4,6,8,10….is an arithmetic sequence with the common difference 2.

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The flowchart to find the biggest of 3 numbers is mentioned below:

A flowchart is a type of diagram that represents an algorithm, process, or workflow. It is a visual representation of the steps and decisions involved in a problem-solving or decision-making process. Flowcharts use a variety of symbols and shapes to represent different types of steps and decisions, such as inputs, outputs, process steps, and decision points. They are used to communicate the logic of a program or process to different stakeholders, such as developers, managers, and users.

An algorithm is a set of instructions or a step-by-step procedure for solving a problem or completing a task. It is a well-defined sequence of operations or actions that are taken in order to achieve a specific goal or outcome. Algorithms can be expressed using natural language, pseudocode, or programming languages. The steps in an algorithm must be unambiguous and have a clear stopping point.

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10 equally sized slices of the spinner's 250 results. 25 times were made by Diane's dial. 12 spins are for 208.33333333333334 .

12 spins are for 208.33333333333334, 5 spins are worth 500, and 8 spins are worth 312.5. There are eight possibilities each time you spin the spinner (1-8). One of these eight options is for you to land on the number 8. In this case, the probability is 18.

If you spin three times and fall on red (or any other colour), the likelihood is 3/30. The likelihood that the spinner will land on an even number is 5/10. The ratio of the number of "1s" to all the other numbers on the spinner determines this probability. The spinner has a total of 8 numbers on it. The spinner has three ones on it.

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Answer: 15

Step-by-step explanation: In ΔNOP,

m

∠

N

=

(

9

x

+

8

)

∘

m∠N=(9x+8)

∘

,

m

∠

O

=

(

4

x

+

13

)

∘

m∠O=(4x+13)

∘

, and

m

∠

P

=

(

2

x

−

6

)

∘

m∠P=(2x−6)

∘

. Find

m

∠

N

.

m∠N

Answer: A

Step-by-step explanation:

Based on the graph, we know that it is positive if it is above the x-axis. It is also indicated by the positive labels.

A: correct

Looking at choice A, it says the interval is from -2<x<-1. This means we have to find x=-2 and x=-1. On the graph, that interval is above the x-axis, so it is positive.

B: incorrect

Looking at choice B, it says the interval is from -1<x<0. This means we have to find x=-1 and x=1. On the graph, that interval is below the x-axis, so it is negative.

C: incorrect

Looking at choice C, it says the interval is from 0<x<1. This means we have to find x=0 and x=1. On the graph, that interval is below the x-axis, so it is negative.

Therefore, A is the correct answer.

The distance between two points A and B is 5 units.

The number of positive two-digit integers that are multiples of 5 and 7 are 2

In mathematics, multiples are the results of multiplying an integer by a given number.

The multiples of 5 and 7 within 10 to 100 are

35 and 70

multiples of 5: 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

multiples of 7: 7 14 21 28 35 42 49 56 63 70 77 84 91 98

The common numbers are 2 which are 35 and 70

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The required dimensions are solved using linear pair and vertical angle to get the result as

The value of x and y is calculated using linear pair theorem, the theorem implies that

solving for x

(3x + 5) + (x + 15) = 180

3x + x + 5 + 15 = 180

collecting like terms

4x = 180 - 15 - 5

4x = 160

x = 40

solving for y

(y + 20) + (4y - 15) = 180

y + 4y + 20 - 15 = 180

collecting like terms

5y = 180 - 20 + 15

5y = 175

y = 35

Angle AED

= 3x + 5

= 3 * 40 + 5

= 125 degrees

Angle AED = angle CEB = 125 degrees (vertical angles)

Angle DEB

= x + 15

= 40 + 15

= 55 degrees

Angle DEB = Angle AEC = 55 degrees (vertical angles)

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According to the use and the fundamental knowledge behind these formulas, The top 5 formulas in mathematics are quadratic, Pythagorean , slope-intercept , exponential and Euler's Formula.

Mathematics is the study of numbers, shapes, and patterns. It is the science of studying the properties and relationships of quantities and shapes using logic, symbols and mathematical operations. It is a way of understanding the world and solving problems using quantitative reasoning.

A mathematical formula is a set of symbols, numbers and mathematical operations that express a relationship or equation. These formulas are used to model, describe and explain phenomena in the natural and physical world, as well as in abstract mathematical theories. Formulas can take many forms, including equations, identities, and inequalities. They allow us to make predictions and calculations, and can be used in various fields of science, engineering and other fields to solve problems.

1. root of [tex]ax^2+bx+c[/tex] is [tex]x= \frac {-b+- \sqrt{b^2-4ac}}{2a}[/tex].

2.[tex]h^2 = p^2 +b^2[/tex]

3. [tex]y =mx+c[/tex]

4.[tex]e^x[/tex]

5.[tex]e^{ix} = cosx+isinx[/tex]

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On solving the provided question, we can say that by fraction they will have the same amount of fish in 5 months.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Month / Brent / Gretel

0/4/ 128

1/ 16 / 256

2 / 64 / 512

3 / 256 / 1024

4 / 1024 / 2048

5 / 4096 / 4096

They will have the same amount of fish in 5 months.

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The reasons and responses to the graphs in the question are as follows:

Graph 1.

The amplitude of the first graph is (1/2) which is the height from the midline to the peak

The value of the function at x = 0 is -(1/2), where sin(0) = 0, therefore, the function is a cosine function

The period of the graph is 2·π, which is the period of the parent cosine function

Therefore, the correct option is

Graph 2: Please find attached the graph of the function g(x) = 2×cos(x)

Graph 3: The frequency of a sinusoidal function is given as follows;

The period of the graph = π

Therefore;

The frequency of the sinusoidal graph is 2

Graph 4.  Required:

To find the equation that represents the function of the graph

Solution;

The period of the function, T = π

The graph of the function has a maximum at x = 0, therefore, the graph is similar to a cosine function, y = cos(B·x)

Where;

B = 2·π/T

Therefore;

B = 2·π/π = 2

Therefore;

The equation that represent the function in the graph is f(x) = cos(2·x)

Question 5. The given function is f(x) = cos(2·x)

The frequency factor in the given function, B = 2

The period, T = 2·π/B

Therefore, T = 2·π/2 = π

The period of the function, f(x) = cos(2·x), is 2

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==========================================================

Explanation:

We'll break things up into cases. The phrasing "at least 3" means "3 or more".

We either will have 3 kings or 4 kings.

----------------------------------------------

Case A) There are exactly 3 kings.

Use the nCr combination formula. There are n = 4 kings total and we select r = 3 of them. That gives 4C3 = 4 ways to pick the 3 kings.

Put another way: there are 4 ways to leave a certain king out of the hand.

Then we have 52-4 = 48 cards that aren't a king, and we need to fill the remaining r = 2 slots. Through the nCr formula, you should find that 48C2 = 1128

To recap, we found

That gives 4*1128 = 4512 ways to have case A happen.

----------------------------------------------

Case B) There are exactly 4 kings

4C4 = 1, so there's only one way to select all the kings. The order doesn't matter. Then we have 48 cards to pick from for the fifth slot.

Overall there are 1*48 = 48 ways to have case B play out.

----------------------------------------------

There were 4512 ways to have case A happen, and 48 ways to have case B happen.

These cases are mutually exclusive to allow us to simply add the counts:

4512+48 = 4560

This is why the final answer is 4560

Step-by-step explanation:

this is a multiplication dot, right ?

so,

(f.g)(x)

or

(f×g)(x)

any arithmetic operation (like +, -, ×, ÷) between 2 functions is done by applying that operation to the functional expressions.

(f×g)(x) = (x² - 12x + 35)(x - 5) =

= x³ - 5x² - 12x² + 60x + 35x -175 =

= x³ - 17x² + 95x - 175

Step-by-step explanation:

(f.g)(x) = f(x) . g(x)

= (x² - 12x + 35)(x - 5)

=x(x²-12x+35) - 5(x²-12x+35)

= x³-12x²+35x-5x²+60x-175

(f.g)(x)=x³-17x²+95x-175

The corresponding element in the range when 7 is an element  in the domain is f(7)=33

Step-by-step explanation:

Given that the 7 is an element in the domain of f(x)

The function f is defined by f(x)=6x-18/2

To find the corresponding element in the range:

That is put x=7 in the given function f(x)

Therefore f(x) becomes

f(7) = 6(7)-18/2

      =42-18/2

      =42-9

      =33

Therefore corresponding element in the range when 7 is an element  in the domain is f(7)=33

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The quantities which are proportional to 12/4 are 36/12 and 3/1 .

What is proportional ?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.

The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.

12/4 ⇒ 3/1

          = 24/9

          = 8/3

The quantity 12/4 is not proportional to 48/18

        = 18/6

        = 3/1

The quantity 12/4 is proportional to 36/12

       = 7/3

The quantity 12/4 is not proportional to 35/15

       = 12/8

       = 6/4

       = 3/2

The quantity 12/4 is not proportional to 24/16

The quantity 12/4 is proportional to 3/1

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Answer:

The values are 13 and 1

I hope this is correct

The ladder would reach a distance of 6 feet up the wall.

This is a theorem that can be used to determine the unknown side of a right angled triangle. It is given as:

/hyp/^2 = /opp/^2 + /adj/^2

In the given question, the ladder is placed a against a vertical wall of a building. Given that the bottom of the ladder is 8 feet to the base of the building. Therefore this is would form a right angled triangle, such that the Pythagorean theorem can be applied.

So that, let the height of the ladder on the wall be represented by t. Then;

10^2 = t^2 + 8^2

100 = t^2 + 64

t^2 = 100 -64

     = 36

t = (36)^1/2

t = 6 feet

Thus the ladder is placed 6 feet up the vertical wall.

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Answer:

n0p = 120°

Step-by-step explanation:

m0n + n0p = 180°

60° + n0p = 180°

n0p = 120°

The combined gas law for a gas is discussed below.

Given is the combined gas law.

The ideal combined gas law is given by →

PV = nRT

Where -

{P} = pressure     {T} = temperature     {V} = volume    

{n} = number of moles   {R} = gas constant

Non ideal gases are often modelled by the Van der Waals equation as →

(p + n²a/V²)(V - nb) = nRT

Where -

{a} and {b} = constants for a particular gas

{p} = pressure       {v} = volume    

{n} = number of moles       {t} = temperature  

{R} = gas constant

Therefore, the combined gas law for a gas is discussed above.

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The conditions for inference are: The customers who are surveyed are chosen independently at random, so we can assume that the survey results are independent.

The amount of grams or mole equivalents of solute present in a solution that contains one liter is what is referred to as normalcy according to the accepted definition. The amount of moles of reactive units in a compound is what we mean when we say it is equal.

The conditions for inference are met.

However, to conclude that more than 50% of customers who dine at his restaurant would rate the food as excellent, we need to conduct a statistical test such as a one-sample proportion test or a confidence interval. The manager would need to compare the proportion of the customers who rated the food as excellent from the survey with the proportion of customers who would rate the food as excellent. This would allow to see if the data provides convincing evidence that more than 50% of customers who dine at his restaurant would rate the food as excellent.

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